For deep and wide quantum circuits, the increase in optimization time is exacerbated by the presence of barren plateaus, or vanishingly small gradients in the energy landscape, where re-initialization can leave one trapped at a position far removed from the minimum [1]}, [2]}, [3]}. Conversely, short time-steps lead to efficient solution trajectories that remain close to the local cost minima, leading to significant reduction in optimization times. To verify this, we conduct numerical simulations varying the diffusion parameter \(\delta \)  with \(l=n\)  up to time \(T=1\) . fig:fig2c shows that the number of iterations, or required optimization steps, per time-step increases linearly with \(\delta \) . Close inspection of the time-averaged trace distance shows bimodal distributions at higher \(\delta \) , which separates success and failure during convergence towards the global minimum (see Fig. REF d, dotted lines), resembling local minima traps due to poor optimization or expressivity of ansätze [4]}, [5]}.
